Do companies actually sue if you break such an NDA? It would be a poster child for the Streissand effect.
One should also consider the size of the company when considering the risks to the pets: "More than 2 million “pet parents” have turned to Rover’s network of “trusted sitters and dog walkers”. Ask 2 million people who had neighbors and friends they trusted take care of their dogs and I think you’d find horror stories as well.
On the other hand, perhaps it is a good thing if companies that get too large accumulate bad news. Prevent monopolies.